For a heap-based priority queue to be at its most effective, the "priority" should be something that can take on a wide range of values (lengths, timestamps, populations). It optimises the tasks of searching the queue for the appropriate place to insert an item (and inserting it); and removing the first item in the list.

Items may potentially be inserted into the queue wherever two adjacent items have different priorities. The heap structure is an efficient way of indexing such insertion points when there are many of them distributed throughout the list.

If you have a sharply-limited enumeration of possible priority values, then there are very few insertion possible insertion points - one for each priority value. In that situation, one can make the insertion points explicit (and thus eliminate the need to maintain a heap indexing them) by implementing your priority queue as a list of simple queues from which you draw successive items from the highest-priority nonempty queue.